Weedon served as a Lieutenant under George Washington in the French and Indian War, mainly assigned to garrison duty in western Virginia. He moved to Fredericksburg and opened a tavern.
In 1775 he was made a Lieutenant Colonel, and tasked with creating the 3rd Virginia regiment. He was promoted to colonel in 1776 and Brigadier General in 1777. He fought in the Battles of Trenton, Brandywine, and Germantown.
At Valley Forge Weedon commanded a brigade in Nathanael Greene's division. His brigade included Stewart's 13th Pennsylvania along with the 2nd, 6th, 10th, and 14th Virginia regiments.
In 1778 he resigned after a dispute with the Congress over seniority. He went home to Virginia, and led a brigade of the state's militia. He fought with his militia unit in the Battle of Yorktown (1781).